Question

Nicole shines a light from a window of a lighthouse on a cliff 250 feet above the water level. Nick 10 feet above the water level in a ship off shore, finds that the angle of elevation of the light is 3°. Find the length of the line of sight (light beam) from the ship to Nicole.

Answer 1

Answer:

4585.8 feet

Step-by-step explanation:

If we draw the triangle, the opposite side to 3° angle would be "10" less than total height of 250 because Nick is 10 feet above water level, so that side will be:

250 - 10 = 240

The hypotenuse of the triangle is the length of line of sight. We can call this "x".

So, using trigonometric ratio of sine (opposite/hypotenuse), we can write:

$Sin(3)=\frac{240}{x}$

Now, we cross multiply and solve for x, line of sight length:

$Sin(3)=\frac{240}{x}\\x=\frac{240}{Sin(3)}\\x=4585.8$